Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 8

Determine whether each function is continuous or discontinuous at the following scenarios and explain why.

(a) The temperature as a function of time at a specific area.
The function is continuous since the temperature changes with respect to time proportionally.

(b) The temperature as a function of time due west from Oklahoma City at a specific time.
The function is continuous since the temperature changes with respect to distance proportionally.

(c) The altitude above sea level as a function of distance due west from Oklahoma City.
The function is discontinuous since the altitude may increase abruptly up to a certain height with respect to the distance.

(d) The fare on a taxi as the function of the distance traveled.
The function is discontinuous since the cost of a taxi ride inccrements on a certain value with respect to the distance.

(e) The Light's current in the circuit as a function of time.
The function is discontinuous because when you turn the light on, the current jumps on a certain value but when you turn it off, the current return to its initial value .